Well, this
time I’ll show you an electronic circuit that I thought was cool. It is called
the CHAOS GENERATOR, why? Because when you see its output in the oscilloscope
in the XY mode you get something like this:
So, it
looks like an electromagnetic field attractor (if you remember some of you
physics classes). And it is said to generate chaos because the circuit does not
seem to set to into a stable mode for a reasonable period of time, that’s why
the XY view looks like the signal moves without control.
The circuit
that I show you here is a variation of the classic phase shift oscillator. And
it is cheap and entertaining for a nothing-to-do afternoon.
Without the
components inside the blue line, the circuit oscillates in a stable way, and
there is a deformed sine wave at the T1 transistor collector. As show in the
Bode diagrams of the classic phase shift oscillator below, the three stages of
the RC ladder shift the phase 180 degrees. So only at the frequency that produces this
phase shift the circuit will oscillate, in this way the total shift around the
loop will be o or 360 degrees (T1 also produces a 180° phase displacement).
For
oscillations to be sustained, the gain K produced by the transistor should be
inverse to the magnitude of the RC network transfer function at the frequency
of oscillation. This is to satisfy the
unity-gain loop condition for oscillators.
Nevertheless,
with the addition of the extra components in the blue line the output is
completely different. When the amplitude increases during the booting of the
oscillator, the transistor T2 will start to conduct at a certain point. This
makes the resistor R5 to join the feedback loop and change the phase relation,
which will force the circuit to find a new point of equilibrium.
To achieve
CHAOS, the circuit should not find a stable situation, but a series of instable
situations very close to each other. These situations are represented by “orbits”
in the oscilloscope forming the so called “attractor.” Playing with the
potentiometer P and the input voltage you can force the circuit to pass from
one stable oscillation to chaos to another stable condition. Also, changing P1,
R5 and C5 influence in the attractor’s shape.
The circuit
contains 4 elements that store energy, for this reason the phase space has 4
dimensions. What we see in the oscilloscope is actually a 2D projection of an
attractor in 4D. We can see other projections connecting the Y and Z instead of
the X and Y points.
Here is a video
compilation of the images I got. You can also see the video in my youtube account: http://www.youtube.com/watch?v=EvB6w3WwP_0&feature=youtu.be










